The increase in the density of semiconductor devices has continued to expand without showing any limits, and the development of various techniques and methods has been pursued in order to realize such a high density. One of these techniques is multi-layer wiring; technical problems that accompany this technique include global flattening of the device surface (i.e., flattening over a relatively large area) and wiring between upper and lower layers.
Considering the shortening of the focal depth during exposure that has accompanied the shortening of the wavelengths used in lithography, there is a great requirement for precision in the flattening of inter-layer layers at least in the range of the exposed area. Furthermore, the requirement for so-called inlay (plug, damascene) which is the embedding of metal electrode layers has also increased for the realization of multi-layer wiring; in this case, the removal of excess metal layers and flattening following lamination must be performed. Chemical mechanical polishing has attracted attention as an efficient flattening technique for such large (die size level) areas. This is a polishing process called CMP (chemical mechanical polishing or planarization). CMP is a process which removes the surface layers of wafers by using a chemical action in combination with physical polishing, and is the strongest candidate for global flattening and electrode formation techniques.
In concrete terms, a polishing agent called a slurry is used in which abrasive grains (generally silica, alumina, cerium oxide or the like) are dispersed in a solvent such as an acid, alkali or oxidizing agent, etc., that can dissolve the object of polishing; furthermore, a polishing tool is used which has an appropriate polishing body (polishing body such as a polishing pad) and a substrate such as a polishing platen that supports the surface of this polishing body on the side opposite the polishing surface so that the wafer surface is pressed by the above-mentioned polishing body, and polishing is caused to proceed by rubbing through a relative motion.
As the use of the above-mentioned polishing body progresses, the polishing capacity drops as a result of clogging of the polishing surface of the polishing body, etc. Conventionally, therefore, dressing of the polishing body has been performed either simultaneously with the polishing process or separately from the polishing process, so that the polishing surface of the polishing body is planed away.
In order to improve the process efficiency of such a CMP polishing process, and in order to improve the precision of the flatness, it is extremely important to predict the amount of polishing with good precision, and to achieve efficient optimization of the polishing conditions (control parameters of the polishing apparatus, etc.) on the basis of the results of this prediction. Accordingly, a simulation relating to CMP has been proposed, for example, in U.S. Pat. No. 5,599,423.
Furthermore, in polishing other than CMP as well, e.g., in general polishing such as the polishing of optical members (lenses, etc.) and the grinding of wafers, the importance of simulations relating to polishing has been recognized, and various simulation methods have been proposed.
In simulations relating to polishing, the prediction of the amount of polishing is fundamental. Furthermore, in the case of various simulations relating to polishing that have been proposed in the past, the prediction of the amount of polishing has been accomplished according to the equation of Preston expressed by equation (1) shown below. In equation (1), h is the amount by which the object of polishing (polished object) is polished (i.e., the amount of polishing), η is the Preston constant, P is the load (pressure applied to the object of polishing), V is the contact relative velocity between the polishing body and the object of polishing (i.e., the contact relative velocity in the partial region where the amount of polishing is to be determined), and t is the polishing time.h=ηPVt  (1)
This equation of Preston is an empirical rule; however, it is considered that this equation allows the determination of the amount of polishing with extremely good precision, and this equation is treated as a fundamental principle, forming the foundation of all simulations relating to polishing.
When the equation of Preston is applied in conventional simulations relating to polishing, the load P is given with the assumption being made that the polishing surface of the polishing body of the polishing tool is always maintained in a flat state with a high degree of precision.
However, as polishing progresses, the polishing body of the polishing tool is very gradually worn away. In addition, as the dressing process progresses, the polishing body of the polishing tool is worn away by a relatively large amount. Furthermore, such wearing processes of the polishing body are not always uniform in all parts of the polishing surface; there is some variation between respective parts of the polishing body. Accordingly, as the use of the polishing body progresses, the thickness of various parts of the polishing body gradually decreases; moreover, indentations and protrusions are generated in the polishing surface of the polishing body. As a result, because of such variations in thickness and generation of indentations and protrusions, the load that is actually applied between individual partial regions of the polished surface of the object of polishing and the polishing surface of the polishing body differs from the load that is applied in a case where the polishing surface of the polishing body is maintained in a flat state with a high degree of precision.
Accordingly, in the case of the above-mentioned conventional simulations relating to polishing, since the load P is given with the assumption being made that the polishing surface of the polishing body of the polishing tool is always maintained in a flat state with a high degree of precision when the equation of Preston is applied, the precision of the simulation of the amount of polishing drops as a result of being affected by the generation of indentations and protrusions in the polishing surface of the polishing body and the like. Specifically, since the effects of the generation of indentations and protrusions in the polishing surface of the polishing body and the like are not taken into account in the above-mentioned conventional simulations relating to polishing, the precision of the simulation of the amount of polishing drops. When the precision of the simulation of the amount of polishing thus drops, it becomes difficult to optimize the polishing conditions (control parameters of the polishing apparatus, etc.) with good efficiency; as a result, it becomes impossible to increase the process efficiency of the CMP polishing process, and the precision of the flatness drops.
The situations described above apply not only to CMP, but also to other types of polishing, e.g., the polishing of optical members such as lenses.